Theorem nfimdOLDOLD 1824

Description: Obsolete proof of nfimd 1823 as of 3-Nov-2021. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 30-Dec-2017.) df-nf 1710 changed. (Revised by Wolf Lammen, 18-Sep-2021.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nfimd.1	|- ( ph -> F/ x ps )
nfimd.2	|- ( ph -> F/ x ch )

Assertion

Ref	Expression
nfimdOLDOLD	|- ( ph -> F/ x ( ps -> ch ) )

Proof of Theorem nfimdOLDOLD

Step	Hyp	Ref	Expression
1		19.35 1805	. . 3 |- ( E. x ( ps -> ch ) <-> ( A. x ps -> E. x ch ) )
2		nfimd.1	. . . . . 6 |- ( ph -> F/ x ps )
3		nf4 1713	. . . . . 6 |- ( F/ x ps <-> ( -. A. x ps -> A. x -. ps ) )
4	2, 3	sylib 208	. . . . 5 |- ( ph -> ( -. A. x ps -> A. x -. ps ) )
5		pm2.21 120	. . . . . 6 |- ( -. ps -> ( ps -> ch ) )
6	5	alimi 1739	. . . . 5 |- ( A. x -. ps -> A. x ( ps -> ch ) )
7	4, 6	syl6 35	. . . 4 |- ( ph -> ( -. A. x ps -> A. x ( ps -> ch ) ) )
8		nfimd.2	. . . . . 6 |- ( ph -> F/ x ch )
9	8	nfrd 1717	. . . . 5 |- ( ph -> ( E. x ch -> A. x ch ) )
10		ala1 1741	. . . . 5 |- ( A. x ch -> A. x ( ps -> ch ) )
11	9, 10	syl6 35	. . . 4 |- ( ph -> ( E. x ch -> A. x ( ps -> ch ) ) )
12	7, 11	jad 174	. . 3 |- ( ph -> ( ( A. x ps -> E. x ch ) -> A. x ( ps -> ch ) ) )
13	1, 12	syl5bi 232	. 2 |- ( ph -> ( E. x ( ps -> ch ) -> A. x ( ps -> ch ) ) )
14	13	nfd 1716	1 |- ( ph -> F/ x ( ps -> ch ) )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1481   E.wex 1704   F/wnf 1708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)